logsort.h

/*
 * 
MIT License

Copyright (c) 2022-2024 aphitorite

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
 *
 */
 
#ifndef LOGSORT_H
#define LOGSORT_H

#include <stdlib.h>
#include <string.h>

#define MIN_SMALLSORT 7
#define MIN_PIPOSORT 512

char log_ceil_log(size_t n) {
	char r = 0;
	while((1 << r) < n) r++;
	return r;
}

////////////////
//            //
//  PIPOSORT  //
//            //
////////////////

// courtesy of @scandum's piposort

void log_smallsort(VAR *array, size_t nmemb)
{
	VAR swap, *pta, *pte;
	unsigned char w = 1, x, y, z = 1;

	switch (nmemb) {
	default:
		pte = array + nmemb - 3;
		
		do {
			pta = pte + (z = !z);

			do {
				x = cmp(pta, pta + 1) > 0; y = !x; 
				swap = pta[y]; pta[0] = pta[x]; pta[1] = swap; 
				pta -= 2; w |= x;
			}
			while(pta >= array);
		}
		while(w-- && --nmemb);
		return;
		
	case 3:
		pta = array;
		
		x = cmp(pta, pta + 1) > 0; y = !x; 
		swap = pta[y]; pta[0] = pta[x]; pta[1] = swap; pta++;
		
		x = cmp(pta, pta + 1) > 0; y = !x; 
		swap = pta[y]; pta[0] = pta[x]; pta[1] = swap;
		
		if(x == 0) return;
		
	case 2:
		pta = array;
		
		x = cmp(pta, pta + 1) > 0; y = !x; 
		swap = pta[y]; pta[0] = pta[x]; pta[1] = swap;
		
	case 1:
	case 0:
		return;
	}
}

void log_parity_merge(VAR *from, VAR *dest, size_t left, size_t right) {
	VAR *ptl, *ptr, *tpl, *tpr, *tpd, *ptd;
	unsigned char x;

	ptl = from; ptr = from + left; ptd = dest;
	tpl = from + left-1; tpr = from + left+right-1; tpd = dest + left+right-1;

	if(left < right) *ptd++ = CMP(ptl, ptr) <= 0 ? *ptl++ : *ptr++;

	while(--left) {
		x = CMP(ptl, ptr) <= 0; *ptd = *ptl; ptl += x; ptd[x] = *ptr; ptr += !x; ptd++;
		x = CMP(tpl, tpr) <= 0; *tpd = *tpl; tpl -= !x; tpd--; tpd[x] = *tpr; tpr -= x;
	}
	*tpd = CMP(tpl, tpr)  > 0 ? *tpl : *tpr;
	*ptd = CMP(ptl, ptr) <= 0 ? *ptl : *ptr;
}
void log_piposort(VAR *array, VAR *swap, size_t n) {
	size_t q1, q2, q3, q4, h1, h2;

	if(n <= MIN_SMALLSORT) {
		log_smallsort(array, n);
		return;
	}
	h1 = n/2;  q1 = h1/2; q2 = h1-q1;
	h2 = n-h1; q3 = h2/2; q4 = h2-q3;

	log_piposort(array, swap, q1);
	log_piposort(array + q1, swap, q2);
	log_piposort(array + h1, swap, q3);
	log_piposort(array + h1 + q3, swap, q4);

	if(CMP(array + q1-1, array + q1) <= 0 && 
	   CMP(array + h1-1, array + h1) <= 0 && 
	   CMP(array + h1+q3-1, array + h1+q3) <= 0)
		return;

	log_parity_merge(array, swap, q1, q2);
	log_parity_merge(array + h1, swap + h1, q3, q4);
	log_parity_merge(swap, array, h1, h2);
}

///////////////////////
//                   //
//  PIVOT SELECTION  //
//                   //
///////////////////////

// courtesy of @scandum's blitsort

void log_trim_four(VAR *pta) {
	VAR swap;
	size_t x;

	x = cmp(pta, pta + 1)  > 0; swap = pta[!x]; pta[0] = pta[x]; pta[1] = swap; pta += 2;
	x = cmp(pta, pta + 1)  > 0; swap = pta[!x]; pta[0] = pta[x]; pta[1] = swap; pta -= 2;

	x = (cmp(pta, pta + 2) <= 0) * 2; pta[2] = pta[x]; pta++;
	x = (cmp(pta, pta + 2)  > 0) * 2; pta[0] = pta[x];
}

VAR log_median_of_nine(VAR *a, VAR *s, size_t n) {
	size_t step = (n-1) / 8, i;
	VAR *pa = a;
	
	for(i = 0; i < 9; i++) 
		{ s[i] = *pa; pa += step; }
	
	log_smallsort(s, 9);
	return s[4];
}

VAR log_smart_median(VAR *array, VAR *swap, size_t n, size_t bLen) {
	if(bLen < 64) return log_median_of_nine(array, swap, n);
	
	size_t cbrt;
	for(cbrt = 32; cbrt*cbrt*cbrt < n && cbrt < 1024; cbrt *= 2) {}
	
	size_t div = bLen < cbrt ? bLen : cbrt;
	size_t step = n/div, c;
	VAR *i = array, *j;
	
	// copy sample to swap space
	
	for(c = 0; c < div; c++) 
		{ swap[c] = *i; i += step; }
	
	// halve the sample using trim fours
	
	div /= 2; i = swap; j = swap + div;
	
	for(c = (div /= 4); c; c--) {
		log_trim_four(i);
		log_trim_four(j);
		
		i[0] = j[1]; i[3] = j[2];
		i += 4; j += 4;
	}
	
	// sort sample for median
	
	div *= 4;
	log_piposort(swap, swap+div, div);
	
	return swap[div/2 + 1];
}

///////////////
//           //
//  LOGSORT  //
//           //
///////////////

void log_block_xor(VAR *a, VAR *b, size_t v) {
	VAR t;
	
	while(v) {
		if(v & 1) { t = *a; *a = *b; *b = t; }
		v >>= 1; a++; b++;
	}
}

#define PIVFUNC(NAME) NAME##_less
#define PIVCMP(a, b) (CMP((b), (a)) > 0)

#include "logPartition.c"

#undef PIVFUNC
#undef PIVCMP

#define PIVFUNC(NAME) NAME##_less_eq
#define PIVCMP(a, b) (CMP((a), (b)) <= 0)

#include "logPartition.c"

#undef PIVFUNC
#undef PIVCMP

// logsort sorting functions

void logsort_rec(VAR *a, VAR *s, size_t n, size_t bLen) {
	size_t minSort = bLen < MIN_PIPOSORT ? bLen : MIN_PIPOSORT;
	
	while(n > minSort) {
		VAR piv = n < 2048 ? log_median_of_nine(a, s, n)
		                   : log_smart_median(a, s, n, bLen);
		
		VAR *p = log_partition_less_eq(a, s, n, bLen, &piv);
		size_t m = p-a;
		
		if(m == n) { // in the case of many equal elements
			p = log_partition_less(a, s, n, bLen, &piv);
			n = p-a;
			
			continue;
		}
		logsort_rec(p, s, n-m, bLen);
		n = m;
	}
	log_piposort(a, s, n);
}
void logsort(VAR *a, size_t n, size_t bLen) {
	if(n < bLen) bLen = n;
	if(bLen < 9) bLen = 9; // for median of nine
	
	VAR *s = malloc(bLen * sizeof(VAR));
	logsort_rec(a, s, n, bLen);
	free(s);
}

#undef MIN_SMALLSORT
#undef MIN_PIPOSORT

#endif // LOGSORT_H